The polynomial remainder theorem says that a polynomial p(x) leaves a remainder of p(k) when it's divided by x - k.
We're given that dividing p(y) = 2y³ + by² - cy + d leaves the same remainder R after dividing it by y + 1, y - 2, and 2y - 1. So we have
p(-1) = 2(-1)³ + b(-1)² - c(-1) + d = R
==> R = -2 + b + c + d
p(2) = 2(2)³ + b(2)² - c(2) + d = R
==> R = 16 + 4b - 2c + d
p(1/2) = 2(1/2)³ + b(1/2)² - c(1/2) + d = R
==> R = 1/4 + b/4 - c/2 + d
We're also given that y + 2 is a factor, which means dividing p(y) by it leaves no remainder, and so
p(-2) = 2(-2)³ + b(-2)² - c(-2) + d = 0
==> 0 = -16 + 4b + 2c + d
Solve the system of equations in boldface. You can eliminate d from the first 3 to first solve for b and c, then solve for d :
(-2 + b + c + d) - (16 + 4b - 2c + d) = R - R
-18 - 3b + 3c = 0
b - c = -6
(-2 + b + c + d) - (1/4 + b/4 - c/2 + d) = R - R
-9/4 + 3b/4 + 3c/2 = 0
b + 2c = 3
(b - c) - (b + 2c) = -6 - 3
-3c = -9
c = 3
b - 3 = -6
b = -3
-16 + 4(-3) + 2(3) + d = 0
d = 22
In 9.3 x 10-8 the exponent is a negative number. Which of these describes the value of a number in scientific notation that includes a negative exponent
Answer:
0.000000093
Step-by-step explanation:
Theres seven zeros after the decimal
if 2m-6=8m them 3m= what
Answer:
C. -3
Step-by-step explanation:
First, you would subtract 2m on both sides in the first equation, to get 6m = -6. Since you wan to find 3m, just divide -6 by 2 to get -3.
Mason prepared 12 kilograms of dough after working 3 hours. How many hours did Mason
work if he prepared 20 kilograms of dough? Solve using unit rates.
Identify if each given value is a zero of the equation 0=18c3−50c
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[tex]18 {c}^{3} - 50c = 0 [/tex]
[tex]2c(9 {c}^{2} - 25) = 0 [/tex]
[tex]2c(3c + 5)(3c - 5) = 0[/tex]
_________________________________
[tex]2c = 0[/tex]
[tex]c = 0[/tex]
_________________________________
[tex]3c + 5 = 0[/tex]
[tex]c = - \frac{5}{3} \\ [/tex]
_________________________________
[tex]3c - 5 = 0[/tex]
[tex]c = \frac{5}{3} \\ [/tex]
Done...
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The only zero of the equation 0=18c³−50c is c = 0, as it makes the equation true when substituted.
value is a zero of the equation 0 = 18c³ - 50c,
putting in the value for c
If c = 0:
0 = 18(0)³ - 50(0)
0 = 0 - 0
0 = 0 (True)
If c = 2:
0 = 18(2)³ - 50(2)
0 = 18(8) - 100
0 = 144 - 100
0 = 44 (False)
If c = -1:
0 = 18(-1)³ - 50(-1)
0 = 18(-1) + 50
0 = -18 + 50
0 = 32 (False)
only c = 0 is a zero of the equation 0 = 18c³ - 50c.
The equation 0 = 18c³ - 50c has only one zero, which is c = 0, as it satisfies the equation when substituted.
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How many significant figures are in the number 0.00282
Step-by-step explanation:
has 3 (sig figs) and 5 decimals. see the additional (+) and subtraction (-) round by the last number of decimals or use scientific no ( e.g. 1.000 x 10^3 or 1.000e3)
In a certain community, 8% of all adults over 50 have diabetes. If a health service in this community correctly diagnoses 95% of all persons with diabetes as having the disease and incorrectly diagnoses 2% of all persons without diabetes as having the disease, find the probabilities that
a) the community health service will diagnose an adult over 50 as having diabetes.
b) a person over 50 diagnosed by the health service as having diabetes actually has the disease.
Answer and Step-by-step explanation:
Solution:
Given:
Let A is the event of a person over 50 diagnosed by health service.
B1 is the event that an adult over 50 actually has diabetes.
B2 is the event that an adult over 50 does not have diabetes.
P (B1) = 8% = 0.08
And P (B2) = 1 – P (B1)
= 1 – 0.08
= 0.92
Correctly diagnose of all persons with diabetes= 95%
P (A/B1) = 0.95
Incorrectly diagnose of all persons without diabetes= 2%
P (A/B2) = 0.02
(a) ) the community health service will diagnose an adult over 50 as having diabetes.
P (B1) P (A/B1) = (0.08) (0.95) = 0.076
P (B2) p (A/B2) = (0.92) (0.02) =0.0184
P (B1) P (A/B1) + P (B2) p (A/B2) = 0.076 + 0.0184
= 0.0944
(b) A person over 50 diagnosed by the health service as having diabetes actually has the disease.
By using formula:
P (B1/A) = P (B1) P (A/B1) / P (B1) P(A/B1) + P (B2) P (A/B2)
Put all the given values:
= (0.08) (0.95) / (0.08) (0.95) + (0.92) (0.02)
=0.076 / 0.076 + 0.0184
=0.076 / 0.0944
= 0.8050
Using conditional probability, it is found that there is a:
a) 0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.
b) 0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.Item a:
The percentages of a positive test is:
95% of 8%(have diabetes).2% of 92%(do not have diabetes).Hence:
[tex]P(A) = 0.95(0.08) + 0.02(0.92) = 0.0944[/tex]
0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.
Item b:
Event A: Positive test.Event B: Has the disease.From item a, [tex]P(A) = 0.0944[/tex].
The probability of both a positive test and having the disease is:
[tex]P(A \cap B) = 0.95(0.08)[/tex]
Hence, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.95(0.08)}{0.0944} = 0.8051[/tex]
0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.
A similar problem is given at https://brainly.com/question/14398287
out of fifty students,34 joined the journalism class and 25 joined robotics club.if 16 students joined both clubs,how many students are in neither club?how many are in either club? show the venn diagram
Answer:
Step-by-step explanation:
Total student=50
35 -> j.
25 -> r.
16-> j.+r.
35-16=19 students joined j.
25-16=9 joined r.
50-19+9
50-28=22
Awnser is 22
It will be nice if you give me brainliest. Good luck!
What is the apparent range of the function of x shown?
A) The set of all real numbers greater than or equal to 1
B) The set of all real numbers less than or equal to 1
C) The set of all real numbers greater than or equal to 4
D) The set of all real numbers
(PLEASE LOOK AT THE PICTURE BEFORE ANSWERING)
A tennis racket is normally priced at 90.00 is on for 30% off. What is an expression for the sale price of the racket,
Answer:
90×0.7
Step-by-step explanation:
I think this is the correct answer.
100-30=70
70=0.7
Calculate the area of the triangle: A =
Answer:
27
Step-by-step explanation:
The area of the triangle is 30.9 square units.
We have,
From the figure,
Height = Distance between (-2, 6) and (-2, 0).
Base = Distance between (-2, 0) and (7, -5).
To find the distance between two points in a Cartesian coordinate system, use the distance formula:
Distance = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]
Height:
Distance = √((-2 - (-2))² + (0 - 6)²)
Distance = √(0² + (-6)²)
Distance = √(0 + 36)
Distance = √36
Distance = 6
Base:
Distance = √((7 - (-2))² + (-5 - 0)²)
Distance = √((7 + 2)² + (-5)²)
Distance = √(9² + (-5)²)
Distance = √(81 + 25)
Distance = √106
Distance ≈ 10.3
Now,
The area of the triangle.
= 1/2 x base x height
= 1/2 x 10.3 x 6
= 10.3 x 3
= 30.9 square units
Thus,
The area of the triangle is 30.9 square units.
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I need help with the table it’s due today pls help ❗️❗️
It’s for culinary arts and hospitality honors
Answer: Eventually you memorize these measurements if you are in cullinary arts.
Step-by-step explanation:
Chart attached, I hope!
The perimeter, P, of a square whose side length is n.
Answer: p = 4n
Step-by-step explanation:
To find the perimeter of a shape, you need to add the length of the 4 sides. A square's 4 sides are equal. Therefore, you add n+n+n+n which is the same as 4n.
Answer:
P = n4
Step-by-step explanation:
in order to find the perimeter of an object you must add up all the sides. since we are dealing with a square all the sides are n. so in conclusion, 4 times n would you get you the perimeter, P.
9) Express the ratio 18:30 in lowest terms.
Answer:
3:5
Step-by-step explanation:
take the biggest common factor which would be 6 in this case, and just divide the two out by that. 3:5
Money that is collecting interest in a bank account doubles in value every 8
years.
When the account was opened, it had 8, or 23 dollars in it. After 32 years, the
account balance has doubled 4 times, increasing by a factor of 24,
It now has a balance of 23. 24. Expressed as a power, how much money, in
dollars, is in the account after 32 years?
A. 24
d
B. 27
C. 212
D. 47
Answer:
2 to the power of 7
Step-by-step explanation:
add the powers when it is multiplication
Is it carbohydrate, lipid, protein, or nucleic acid?
PLEASE HELP!!! LAST QUESTION AND IM STUCKK.
Answer:
nucleic acid
Step-by-step explanation:
Which polynomial represents the area?
Answer:
A is the Answer.
Step-by-step explanation:
You multiply x with 2x ( Gives you 2x^2 ) then -1 with 2x ( Gives you -2x ) then -8 with x ( Gives you -8x ) then -1 with-8 ( Gives you +8 ), finally you add the two x's ( not x^2 ). Your fibal answer will be 2x^2 - 10x +8.
Hope this helps.
What are the x and y-intercepts from the table shown?
Can somebody pls answer these three questions ASAPPPP!!!!
Answer:
1) x = 3/2 2) x = 6 3) x = 3
Step-by-step explanation:
For Number 1:
4(x+8)−4=34
Step 1: Simplify both sides of the equation.
4(x+8)−4=34
(4)(x)+(4)(8)+−4=34(Distribute)
4x+32+−4=34
(4x)+(32+−4)=34(Combine Like Terms)
4x+28=34
Step 2: Subtract 28 from both sides.
4x=6
Step 3: Divide both sides by 4.
4x/4 = 6/4
x = 3/2
For Number 2:
2/3(9+x)=−5(4−x)
Step 1: Simplify both sides of the equation.
6 + 2/3x = −20+5x
Step 2: Subtract 5x from both sides.
−13 /3 x+6=−20
Step 3: Subtract 6 from both sides.
-13/3x = -26
Step 4: Multiply both sides by 3/(-13)
x = 6
For Number 3:
−3(x+4)+15=6−4x
Step 1: Simplify both sides of the equation.
−3(x+4)+15=6−4x
(−3)(x)+(−3)(4)+15=6+−4x(Distribute)
−3x+−12+15=6+−4x
(−3x)+(−12+15)=−4x+6(Combine Like Terms)
−3x+3=−4x+6
−3x+3=−4x+6
Step 2: Add 4x to both sides.
−3x+3+4x=−4x+6+4x
x+3=6
Step 3: Subtract 3 from both sides.
x+3−3=6−3
x = 3
2/3 x - 1 = 9 - 1/6 x Im supposed to solve but i need some help
Answer:
x=12
Step-by-step explanation:
collect the x stuff on one side
2/3 x + 1/6 x = 9 + 1
5/6 x = 10
x = 12
Answer:
x=12
Step-by-step explanation:
first, you need to get the variable to one side
the easiest way to do it and not deal with negatives would be this way:
2/3x - 1 = 9 - 1/6x
+1/6x +1/6x in order to do this you must first convert the 2/3 to 4/6
to then get
5/6x - 1 = 9
then solve it like normal
5/6x - 1 = 9
+1 +1
5/6x = 10
/ 5/6 /5/6
x=12
Evaluate the expression 12-3y\2 + y(2y-4\y) for y =3
Answer:
43/2
Step-by-step explanation:
Evaluate 12 - (3 y)/2 + y (2 y - 4/y) where y = 3:
12 - 3 y/2 + y (2 y - 4/y) = 12 - 3×3/2 + 3 (2×3 - 4/3)
Hint: | Express -3×3/2 as a single fraction.
-3×3/2 = (-3×3)/2:
12 + (-3×3)/2 + 3 (2×3 - 4/3)
Hint: | Multiply 2 and 3 together.
2×3 = 6:
12 - (3×3)/2 + 3 (6 - 4/3)
Hint: | Multiply -3 and 3 together.
-3×3 = -9:
12 + (-9)/2 + 3 (6 - 4/3)
Hint: | Put the fractions in 6 - 4/3 over a common denominator.
Put 6 - 4/3 over the common denominator 3. 6 - 4/3 = (3×6)/3 - 4/3:
12 - 9/2 + 3 (3×6)/3 - 4/3
Hint: | Multiply 3 and 6 together.
3×6 = 18:
12 - 9/2 + 3 (18/3 - 4/3)
Hint: | Subtract the fractions over a common denominator to a single fraction.
18/3 - 4/3 = (18 - 4)/3:
12 - 9/2 + 3 (18 - 4)/3
Hint: | Subtract 4 from 18.
| 1 | 8
- | | 4
| 1 | 4:
12 - 9/2 + 3×14/3
Hint: | Express 3×14/3 as a single fraction.
3×14/3 = (3×14)/3:
12 - 9/2 + (3×14)/3
Hint: | Cancel common terms in the numerator and denominator of (3×14)/3.
(3×14)/3 = 3/3×14 = 14:
12 - 9/2 + 14
Hint: | Put the fractions in 12 - 9/2 + 14 over a common denominator.
Put 12 - 9/2 + 14 over the common denominator 2. 12 - 9/2 + 14 = (2×12)/2 - 9/2 + (2×14)/2:
(2×12)/2 - 9/2 + (2×14)/2
Hint: | Multiply 2 and 12 together.
2×12 = 24:
24/2 - 9/2 + (2×14)/2
Hint: | Multiply 2 and 14 together.
2×14 = 28:
24/2 - 9/2 + 28/2
Hint: | Add the fractions over a common denominator to a single fraction.
24/2 - 9/2 + 28/2 = (24 - 9 + 28)/2:
(24 - 9 + 28)/2
Hint: | Evaluate 24 + 28 using long addition.
| 1 |
| 2 | 8
+ | 2 | 4
| 5 | 2:
(52 - 9)/2
Hint: | Subtract 9 from 52.
| 4 | 12
| 5 | 2
- | | 9
| 4 | 3:
Answer: 43/2
Miss Young is making fruit baskets to send to her 7 cousins. in each basket she puts a g green apples. she puts three times as many red apples in each basket.
Which expression represents the total number of apples Miss Young sends her cousins. choose all that apply.
g +3g
7(g+3g)
7+g+3g
7g+7(3g)
28g
7+4g
Answer: 7(g + 3g) , 7g + 7(3g) , and 28g
Step-by-step explanation: I got it wrong and it showed me the answers so here you go
ABC was translated Find A
Answer:
A' (2, -1)
Explanation:
The object's point A has a coordinate of (-2, 4).
The translation rule states that you:
- Add the x coordinate by 4 (x + 4)
- Subtract the y coordinate by 5 (y - 5)
Substitute the rule to point A's coordinate (x = -2 and y = 4).
(-2 + 4 , 4 - 5) = (2, -1)
Notice that the image's point A has moved four steps to the right and down by five steps from the original object.
Simplify to zero answers.
Kelly can type 120 words in 3 minutes. At that rate, how many words can she type in 5 minutes?
450,137,879 dived by 4,890 please give me step by step explanation please!!
Answer:
92052.73599
Step-by-step explanation:450,137,879 divded by 4,890 you'll get 4,890
I need help math is a pain
Answer:
The answer is A because A has 9 zeroes behind 3.5
triangles EFG and JKL are congruent then which two segments must be congruent?
EF = JK
FG = KL
LJ = GE
Here you go.
mike is 46 yrs old. He is 4 yrs older than 3 times his son Jared's age. Find Jared's age
Answer:
Jared is 14 years old
Step-by-step explanation:
"if A, then B" is the form of a _______statement
The last awnser is 1/21 btw pls help me thank u if you do and u get brainles
Answer:
2/121, 1/121
Step-by-step explanation:
Problem 1:
We have the following letters in the bag:
P R O B A B I L I T Y
There is a total of 11 letters.
If we select B, we have a 2/11 chance to get it. If we then replace it and select A, we have a 1/11 chance to select it.
Thus we have a (2/11) * (1/11) chance to get that combination,
Which is 2/121.
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Problem 2
We have the following letters in the bag:
P R O B A B I L I T Y
There is a total of 11 letters. If we select P, we have a 1/11 chance to get it. If we then replace it and select L, we have a 1/11 chance to select that.
Thus we have a (1/11) * (1/11) chance to get that combination,
Which is 1/121.